Problem: Multiply. $0.9 \times 0.35 = $
Solution: $9 \times 35$ and $0.9 \times 0.35$ multiply the same digits in the same order. So, the product of both problems will also have the same digits in the same order. Let's multiply $9 \times 35$. Then we can estimate to place the decimal point in the product of $0.9 \times 0.35 $. $\begin{aligned} 35&\\ \underline{ \times 9}&\\ 45}\\ \underline{+270}}\\ 315 \end{aligned}$ Let's estimate to place the decimal in $0.9 \times 0.35$. $\begin{aligned} 0.9 \times 0.35 &\approx 0.9 \times 0.4\\\\ &\approx \dfrac{9}{10}\times \dfrac{4}{10}\\\\ &\approx \dfrac{36}{100}\\\\ &\approx 0.36 \end{aligned}$ Where can we place the decimal in $315$ to get a product close to $0.36$ ? $0.9 \times 0.35 = 0.315$